15.10.7 problem 7

Internal problem ID [3094]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 7
Date solved : Tuesday, March 04, 2025 at 03:58:33 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime }-3 y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=4*diff(diff(diff(y(x),x),x),x)-3*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \left (\left (x c_3 +c_2 \right ) {\mathrm e}^{\frac {3 x}{2}}+c_{1} \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 29

ode=4*D[y[x],{x,3}]-3*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x} \left (e^{3 x/2} (c_2 x+c_1)+c_3\right ) \]

✓ Sympy. Time used: 0.182 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 3*Derivative(y(x), x) + 4*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{- x} + \left (C_{1} + C_{2} x\right ) e^{\frac {x}{2}} \]